非自治ABS方程的双线性化和Casorati行列式解

本文给出可积非自治Adler-Bobenko-Suris(ABS)链方程,并通过适当的变量变换将其转化为非自治离散双线性方程,从而得到Casorati行列式解.为完成解的验证,在附录中,本文给出一系列Casorati行列式平移公式.     

Bilinear Identities and Hirota’s Bilinear Forms for the (γn, σk)-KP Hierarchy

In this paper, we discuss how to construct the bilinear identities for the wave functions of the (γ_n, σ_k)-KP hierarchy and its Hirota’s bilinear forms. First, based on the corresponding squared eigenfunction symmetry of the KP hierarchy, we prove that the wave functions of the (γ_n, σ_k)-KP hierarchy are equal to the bilinear identities given in Sec.3 by introducing N auxiliary parameters z_i, i = 1, 2,?…?, N. Next, we derived the bilinear equations for the tau-function of the (γ_n, σ_k)-KP hierarchy. Then, we obtain the bilinear equations for the taufunction of the mixed type of KP equation with self-consistent sources (KPESCS), which includes both the first and the second type of KPESCS as special cases by setting n = 2 and k = 3. Finally, using the relation between the Hirota bilinear derivatives and the usual partial derivatives, we show the procedure of translating the Hirota’s bilinear equations into the mixed type of KPESCS.     

惯性定律的新证法

本文从实对称矩阵的角度 ,给出了惯性定律的一种新证法 .这种证法可使我们从已给的一个实二次型 f( x1 ,x2 ,… ,xn) =∑ni,j=1aijxixj 的矩阵 A=( aij) n× n的诸元素 ,来直接研究这个二次型的性质的这一体系更加完整 .同时 ,本文还大大地改进了雅可比方法 ,使雅可比的方法更加完美 ,应用更加广泛 .     

Ginzburg-Landau Free Energy of Crystalline Color Superconductors: A Matrix Formalism from Solid-State Physics

The Ginzburg-Landau (GL) free energy of crystalline color superconductors is important for understanding the nature of the phase transition to the normal quark matter and predicting the preferred crystal structure. So far the GL free energy at zero temperature has only been evaluated up to the sixth order in the condensate. To give quantitative reliable predictions we need to evaluate the higher-order terms. In this work, we present a new derivation of the GL free energy by using the discrete Bloch representation of the fermion field. This derivation introduces a simple matrix formalism without any momentum constraint, which may enable us to calculate the GL free energy to arbitrary order by using a computer.     

Highly Stable Double‐Stranded DNA Containing Sequential Silver(I)‐Mediated 7‐Deazaadenine/Thymine Watson–Crick Base Pairs

The oligonucleotide d(TX)₉, which consists of an octadecamer sequence with alternating non‐canonical 7‐deazaadenine (X) and canonical thymine (T) as the nucleobases, was synthesized and shown to hybridize into double‐stranded DNA through the formation of hydrogen‐bonded Watson–Crick base pairs. dsDNA with metal‐mediated base pairs was then obtained by selectively replacing W‐C hydrogen bonds by coordination bonds to central silver(I) ions. The oligonucleotide I adopts a duplex structure in the absence of Ag⁺ ions, and its stability is significantly enhanced in the presence of Ag⁺ ions while its double‐helix structure is retained. Temperature‐dependent UV spectroscopy, circular dichroism spectroscopy, and ESI mass spectrometry were used to confirm the selective formation of the silver(I)‐mediated base pairs. This strategy could become useful for preparing stable metallo‐DNA‐based nanostructures.     

Weighted estimates for bilinear fractional integral operators

Moen (2016) proved weighted estimates for the bilinear fractional integrals where . We improve his results when and consider the case . As a corollary we obtain a bilinear Stein–Weiss inequality where .     

Oligonucleotide Analogues with Integrated Bases and Backbones. Part 23

The sulfone 2 , and the sulfoxides (S)‐ 3 and (R)‐ 3 were obtained by oxidation of the thiomethylene‐linked A*[s ]U dinucleoside 1 . Conformational analysis and association studies of 2 , (S)‐ 3 , and (R)‐ 3 reveal a strong influence of the configuration on the conformation of the linking unit and on the self‐association of the dinucleosides.     

High-Temperature Quantum Tunneling and Hydrogen Bonding Rearrangements Characterize the Solid-Solid Phase Transitions in a Phosphonium-Based Protic Ionic Liquid

We report the complex phase behavior of the glass forming protic ionic liquid (PIL) d3-octylphosphonium bis(trifluoromethylsulfonyl)imide [C₈H₁₇PD₃][NTf₂] by means of solid-state NMR spectroscopy. Combined line shape and spin relaxation studies of the deuterons in the PD₃ group of the octylphosphonium cation allow to map and correlate the phase behavior for a broad temperature range from 71 K to 343 K. In the solid PIL at 71 K, we observed a static state, characterized by the first deuteron quadrupole coupling constant reported for PD₃ deuterons. A transition enthalpy of about 12 kJ mol⁻¹ from the static to the mobile state with increasing temperature suggests the breaking of a weak, charge-enhanced hydrogen bond between cation and anion. The highly mobile phase above 100 K exhibits an almost disappearing activation barrier, strongly indicating quantum tunneling. Thus, we provide first evidence of tunneling driven mobility of the hydrogen bonded P−D moieties in the glassy state of PILs, already at surprisingly high temperatures up to 200 K. Above 250 K, the mobile phase turns from anisotropic to isotropic motion, and indicates strong internal rotation of the PD₃ group. The analyzed line shapes and spin relaxation times allow us to link the structural and dynamical behavior at molecular level with the phase behavior beyond the DSC traces.     

Theoretical Studies on the Intermolecular Interactions of Potentially Primordial Base‐Pair Analogues

Recent experimental studies on the Watson–Crick type base pairing of triazine and aminopyrimidine derivatives suggest that acid/base properties of the constituent bases might be related to the duplex stabilities measured in solution. Herein we use high‐level quantum chemical calculations and molecular dynamics simulations to evaluate the base pairing and stacking interactions of seven selected base pairs, which are common in that they are stabilized by two N? H???O hydrogen bonds separated by one N? H???N hydrogen bond. We show that neither the base pairing nor the base stacking interaction energies correlate with the reported pK_a data of the bases and the melting points of the duplexes. This suggests that the experimentally observed correlation between the melting point data of the duplexes and the pK_a values of the constituent bases is not rooted in the intrinsic base pairing and stacking properties. The physical chemistry origin of the observed experimental correlation thus remains unexplained and requires further investigations. In addition, since our calculations are carried out with extrapolation to the complete basis set of atomic orbitals and with inclusion of higher electron correlation effects, they provide reference data for stacking and base pairing energies of non‐natural bases.     

Alkylation of complementary ribonucleotides by 1,2‐dodecyl‐epoxide in a micellar environment: a liquid chromatography—electrospray ionization—sequential mass spectrometry investigation

Alkylation of a pair of complementary ribonucleotides, adenosine monophosphate (AMP) and uridine monophosphate (UMP), was accomplished by 1,2‐dodecyl‐epoxide (DE) in a oil‐in‐water microemulsion based on the cationic surfactant Cetyl‐trimethyl‐ammonium‐bromide, providing a suitable catalytic interface for the reagents. Several, often isomeric, alkylation products, bearing one or two hydroxy–dodecyl moieties on their structures, were identified in the reaction mixtures by high‐performance liquid chromatography coupled to electrospray ionization ion trap mass spectrometry. In particular, mass spectrometry (MS)/MS spectra, implemented by extracted ion chromatograms obtained for peculiar MS/MS product ions, indicated alkylation to occur on uracil and on uracil/phosphate OH groups in singly and doubly alkylated UMP, respectively. Adenine NH₂ group and phosphate or ribose OH groups were found to be involved as such (single alkylation) or in combination, in the case of alkylated derivatives of AMP. The reaction of both endocyclic N and C?O groups (tautomerized to C? OH groups) of uracil and the predominance of nucleophilic attack to the more accessible carbon of the DE epoxydic bridge (the only exception being the reaction by the NH₂ group of adenine) were inferred from MS³ spectra with the help of extracted ion chromatograms for specific fragment ions, after their structural characterization. Interestingly, alkylation on one of the uracil C?O groups and, partially, on the adenine NH₂ group, both potentially involved in AMP/UMP base pairing in the micellar environment, were found to be hindered when both ribonucleotides were present in the reaction mixtures. Copyright © 2009 John Wiley & Sons, Ltd.